Elliptic Interface Problems in Axisymmetric Domains. Part I: Singular Functions of Non - Tensorial Type

We study the regularity of solutions of interface problems for the Poisson equation in axisynunetric domains. The Fourier decomposition of the 3D-problem into a sequence of 2D-variational equations end uniform (with respect to the sequence parameter) a prior; estimates of their solutions are derived. Some non-tensorial singular functions describing the behaviour of the solution near interface edges are given and the smoothness of the stress intensity distribution as well as the tangential regularity are characterized in tenns of Sobolev spaces. In a forthcoming part II of this paper, the results will be applied to error estimates of the so-called Fourier-finite-element method for solving approximately elliptic interface problems in 3D.     

Laserspektroskopie

X-Ray spectra and chemical binding     

Wurtzitan (Tetracyclo[5.3.1.12,6.04,9]dodecan)

A new synthesis of wurtzitane (13) is described starting from 2-oxo-protoadamant-4-ene (2). The key intermediate ketone 7 was obtained by regiospecific ring expansion of the β-amino alcohol 6. Entry to the wurtzitane system involved solvolysis of the tricyclic unsaturated mesylate 10 (→11).     

Efficient preparation of nitrosoarenes for the synthesis of azobenzenes

[reaction: see text] Reaction conditions are described for the oxidation of anilines furnishing nitrosoarenes and the synthesis of unsymmetrically substituted azobenzenes. In a comparative study, the catalytic oxidation of methyl 4-aminobenzoate by hydrogen peroxide was investigated, and SeO(2) proved to be superior or equal to methyl trioxorhenium (MTO) and Na(2)WO(4), respectively. Nevertheless, the application of the inexpensive, environmentally friendly, Oxone in a biphasic system proved to be more efficient, and a variety of useful nitrosoarenes for the synthesis of azo compounds were prepared in high yield and purity on a large scale.     

Twista-4,9-diene. Preliminary communication

A synthesis of twista-4,9-diene ( 17 ) from tricyclo[4.3.1.0^3,8]dec-4-en-10-one ( 2 ) is described.     

1,2endo-Trimethylenenorbornane. A novel isomer of adamantane

An easy approach to the novel adamantane isomer 1,2endo-trimethylenenorbornane (2) is described. Starting from a mixture of pent-4-ynylcyclopentadienes 3 the tricyclic monosaturated key intermediate 5 was prepared by intramolecular cycloaddition (→ 4 ) and subsequent regioselective reduction of the C(5), C(6) double bond. The title hydrocarbon 2 was obtained from 5 upon stereoselective hydrogenation by diimide. In addition specifically deuteriated analogues of 2 were prepared applying dideuteriodiimide. Compound 2 rearranged to 2endo, 6endo-trimethylenenorbornane (4-homobrendane, 10 ) in sulfuric acid as well as with aluminium bromide in carbon disulfide.     

A Further Synthetic Approach to the Adamantane Isomer 2, 5-Trimethylenenorbornane (Tricyclo [5.3.0.03,9]decane, 4-Homotwistbrendane)

A further synthetic approach to 2, 5-trimethylenenorbornane ( 1 ; tricycle [5.3.0.0^3,9]decane, 4-homotwistbrendane), a member of the «adamantaneland», is described starting from methyl 5-oxo-2endo-norbornanecarboxylate ( 5 ). The required C2-chain was introduced by a Wittig-Horner reaction and the ring closure of the trimethylene bridge achieved by an acyloin condensation.